5 problems

Erdős–Szemerédi conjecture. For any $g\in\mathbb{N}$, any $\varepsilon>0$ and any set $A\subseteq\mathbb{C}$, one should have

Let $\alpha,\beta,\gamma in (0,1)$ with $\beta \leq \alpha$. Let $A,B,C \subset [0,1]$ be $\delta$-separated sets with $|A| \leq \delta^{-\alpha}$, $|B|=\delta^{-\beta}$, and…

Strong Erdős–Szemerédi conjecture. For every $c>0$ and $\varepsilon>0$, there is a threshold $n_0$ such that, if $n\geq n_0$, then for every $n$-element set of reals $\mathcal{A}$…

Threefold product-of-sums conjecture. For every $\epsilon>0$,

Iterated product-set sum conjecture. The $k$-fold sumset of $A^{(k)}$ should satisfy